The Algorithm of Probability for Node Selection

The Issue

Probably the most asked question is, is my Node still running?
People get nervous when no earnings show up on a daily or weekly basis.
Unfortunately, that is how it is. The more nodes come online, the more the competition to get selected increases.

My personal longest time of not earning, for one Node, is 23 days. My Node was perfectly fine though.

Estimate your Chances

The probability for a Node to be selected to earn in x days, can be calculated using the following formula:

k = number of validators to be rotated each epoch (4)
m = number of shards (8)
S = number of staked nodes (~1,300)
x = number of days

1 - (1 - km/S) ^ (6x)

Using the formula on the current situation generates the following results

Number of Days Probability of being selected in x days
1 13,89%
2 25,85%
3 36,15%
4 45,02%
5 52,65%
6 59,23%
7 64,89%
8 69,77%
9 73,97%
10 77,58%
11 80,70%
12 83,38%
13 85,69%
14 87,68%
15 89,39%
16 90,86%
17 92,13%
18 93,22%
19 94,16%
20 94,98%
21 95,67%
22 96,27%
23 96,79%
24 97,24%
25 97,62%
26 97,95%
27 98,24%
28 98,48%
29 98,69%
30 98,87%
31 99,03%
32 99,16%
33 99,28%
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@Jamie Thanks! :+1:
This question is asked by everyone!
I would be grateful if you would add information about the fact that on average every month everyone will get the same!

3 Likes

I am not a fan of repeating the same information everywhere.
Instead I added the link to a post that explains the process of being selected, which also holds that information. The time span for Nodes to earn more or less the same is a bit longer than one month.
Thanks for bringing it up.

4 Likes

Greatly explained Jamie lets go!

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@Jamie What would you recommend to calculate your probability for being selected if you had more than one node? Should we just take the entire formula times number of nodes?

I threw together this sheet in case others want to check up to date probability.

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Although I can do math, chance calculations confuse me.

Since these are independent events, I think the “times x” only works when x nodes are at the same number of days not earning, which will be very unlikely.

I would go with the average of the percentages. It is still a number though, your 30% chance node could be selected to earn earlier than your 75% chance node.

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